Unsupervised representation learning is a brittle matter. Consider the classic autoencoder (ae)
[1]}, which compresses data \(\mathbf {x}\)  to a low-dimensional representation \(\mathbf {z}\)  from which data is approximately reconstructed. The nonlinearity of the model implies that sometimes small changes to data \(\mathbf {x}\)  gives a large change in the latent representation \(\mathbf {z}\)  (and sometimes not). Likewise, for some data, reconstructions are of low quality, while for others it is near perfect. Unfortunately, the model does not have a built-in quantification of its uncertainty, and we cannot easily answer when the representation is reliable and accurately reflects data.
